Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with \(K_4\)[Fe(CN)\(_6\)] is : \[ {Cu}^{2+}, \, {Fe}^{3+}, \, {Ba}^{2+}, \, {Ca}^{2+}, \, {NH}_4^+, \, {Mg}^{2+}, \, {Zn}^{2+} \]
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In tests with \( {K}_4[{Fe(CN)}_6] \), only certain cations like Cu²⁺, Fe³⁺, and Zn²⁺ give characteristic precipitates. Cations such as Ba²⁺, Ca²⁺, NH₄⁺, and Mg²⁺ typically do not react in this way.
The characteristic precipitates formed with \( K_4[{Fe(CN)}_6] \) are based on the ability of certain cations to form a precipitate with the ferrocyanide ion. The relevant reactions are: Step 1: Identify the cations that give precipitates with \( K_4[{Fe(CN)}_6] \).
1. \( Cu^{2+} \): Forms a blue precipitate of \( Cu_2[{Fe(CN)}_6] \).
2. \( Fe^{3+} \): Forms a blue precipitate of \( Fe_4[{Fe(CN)}_6]_3 \).
3. \( Zn^{2+} \): Forms a white precipitate of \( Zn_2[{Fe(CN)}_6] \). Step 2: Identify the cations that do not give precipitates.
The following cations do not form characteristic precipitates with \( K_4[{Fe(CN)}_6] \): \( Ba^{2+} \), \( Ca^{2+} \), \( NH_4^+ \), and \( Mg^{2+} \) do not react to form precipitates with ferrocyanide. Conclusion: The cations that form characteristic precipitates with \( K_4[{Fe(CN)}_6] \) are \( Cu^{2+} \), \( Fe^{3+} \), and \( Zn^{2+} \), which gives us a total of 3 cations. Thus, the correct answer is \( \boxed{(3)} \).
